Mister Exam

# Least common denominator ((x^3+y^3)/(x+y))/(x^2-y^2)+(2*y)/(x+y)-(x*y)/(x^2-y^2)

An expression to simplify:

### The solution

You have entered [src]
/ 3    3\
|x  + y |
|-------|
\ x + y /    2*y      x*y
--------- + ----- - -------
2    2    x + y    2    2
x  - y             x  - y 
$$- \frac{x y}{x^{2} - y^{2}} + \left(\frac{2 y}{x + y} + \frac{\frac{1}{x + y} \left(x^{3} + y^{3}\right)}{x^{2} - y^{2}}\right)$$
((x^3 + y^3)/(x + y))/(x^2 - y^2) + (2*y)/(x + y) - x*y/(x^2 - y^2)
Fraction decomposition [src]
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General simplification [src]
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Combinatorics [src]
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Combining rational expressions [src]
 3    3       / 2    2\
x  + y  + 2*y*\x  - y / - x*y*(x + y)
-------------------------------------
/ 2    2\
(x + y)*\x  - y /          
$$\frac{x^{3} - x y \left(x + y\right) + y^{3} + 2 y \left(x^{2} - y^{2}\right)}{\left(x + y\right) \left(x^{2} - y^{2}\right)}$$
(x^3 + y^3 + 2*y*(x^2 - y^2) - x*y*(x + y))/((x + y)*(x^2 - y^2))
Assemble expression [src]
                            3    3
/  2        x   \        x  + y
y*|----- - -------| + -----------------
|x + y    2    2|           / 2    2\
\        x  - y /   (x + y)*\x  - y /
$$y \left(- \frac{x}{x^{2} - y^{2}} + \frac{2}{x + y}\right) + \frac{x^{3} + y^{3}}{\left(x + y\right) \left(x^{2} - y^{2}\right)}$$
              3    3
2*y         x  + y           x*y
----- + ----------------- - -------
x + y           / 2    2\    2    2
(x + y)*\x  - y /   x  - y 
$$- \frac{x y}{x^{2} - y^{2}} + \frac{2 y}{x + y} + \frac{x^{3} + y^{3}}{\left(x + y\right) \left(x^{2} - y^{2}\right)}$$
2*y/(x + y) + (x^3 + y^3)/((x + y)*(x^2 - y^2)) - x*y/(x^2 - y^2)
Powers [src]
              3    3
2*y         x  + y           x*y
----- + ----------------- - -------
x + y           / 2    2\    2    2
(x + y)*\x  - y /   x  - y 
$$- \frac{x y}{x^{2} - y^{2}} + \frac{2 y}{x + y} + \frac{x^{3} + y^{3}}{\left(x + y\right) \left(x^{2} - y^{2}\right)}$$
2*y/(x + y) + (x^3 + y^3)/((x + y)*(x^2 - y^2)) - x*y/(x^2 - y^2)
Rational denominator [src]
/ 2    2\ /        / 3    3\               / 2    2\\              2 / 2    2\
\x  - y /*\(x + y)*\x  + y / + 2*y*(x + y)*\x  - y // - x*y*(x + y) *\x  - y /
------------------------------------------------------------------------------
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2 / 2    2\
(x + y) *\x  - y /                               
$$\frac{- x y \left(x + y\right)^{2} \left(x^{2} - y^{2}\right) + \left(x^{2} - y^{2}\right) \left(2 y \left(x + y\right) \left(x^{2} - y^{2}\right) + \left(x + y\right) \left(x^{3} + y^{3}\right)\right)}{\left(x + y\right)^{2} \left(x^{2} - y^{2}\right)^{2}}$$
((x^2 - y^2)*((x + y)*(x^3 + y^3) + 2*y*(x + y)*(x^2 - y^2)) - x*y*(x + y)^2*(x^2 - y^2))/((x + y)^2*(x^2 - y^2)^2)
2.0*y/(x + y) + (x^3 + y^3)/((x + y)*(x^2 - y^2)) - x*y/(x^2 - y^2)
2.0*y/(x + y) + (x^3 + y^3)/((x + y)*(x^2 - y^2)) - x*y/(x^2 - y^2)
Trigonometric part [src]
              3    3
2*y         x  + y           x*y
----- + ----------------- - -------
x + y           / 2    2\    2    2
(x + y)*\x  - y /   x  - y 
$$- \frac{x y}{x^{2} - y^{2}} + \frac{2 y}{x + y} + \frac{x^{3} + y^{3}}{\left(x + y\right) \left(x^{2} - y^{2}\right)}$$
2*y/(x + y) + (x^3 + y^3)/((x + y)*(x^2 - y^2)) - x*y/(x^2 - y^2)
Common denominator [src]
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